Homework: Developing a "Rate of Change" Function $($Day $3)$

Question $1$

Find the derivative for the function $f(x)=-x^3+2x+1.$ Note: Only use methods we have covered in class so far.

$f^{\text{'}}(x)=\frac{d}{dx}(-x^3+2x+1)=7-\frac{d}{dx}(x^3)+\frac{d}{dx}(2x)+\frac{d}{dx}(1)=-3x^2+21$

$f^{\text{'}}(x)=-3x^2+2$

Question $2$

Plug into your most accurate rate of change function $1$ for x $.$ What is the output telling you about the original function $f(x)=-x^3+2x+1.$ Illustrate your thinking by marking up the graph of $f$ below.